Doubly reflected BSDEs with integrable parameters and related Dynkin games

作者：Bayraktar Erhan^*; Yao Song

来源：Stochastic Processes and Their Applications, 2015, 125(12): 4489-4542.

DOI：10.1016/j.spa.2015.07.007

• BSDEs
• Reflected BSDEs
• Doubly reflected BSDEs
• g-evaluation/expectation
• Penalization
• Optimal stopping problems
• Pasting local solutions
• Dynkin games
• Saddle points

We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle L and the upper obstacle U of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by pasting local solutions, and show that the Y-component of the unique solution represents the value process of the corresponding Dynkin game under g-evaluation, a nonlinear expectation induced by BSDEs with the same generator g as the doubly reflected BSDE concerned. In particular, the first time tau* when process Y meets L and the first time gamma* when process Y meets U form a saddle point of the Dynkin game.

• 出版日期2015-12